In the movie, actor Armie Hammer played both identical twins. Zuckerberg's character snidely called them on-screen the "Winklevi."

The twins, along with Divya Narendra, started a company called ConnectU while at Harvard. They say that Zuckerberg stole their idea. Facebook denies these claims.

The three had agreed to a settlement that had been valued at $65 million. But they argue that based on an internal valuation that Facebook did not disclose, they should have received more Facebook shares as part of the deal.

Facebook took in $1.2 billion of revenue in 2010's first nine months, according to documents that Goldman Sachs provided to clients to entice investors in a special fund set up to invest in the giant social networking firm.

The company was valued at $50 billion as part of that transaction.

A lower court had granted Facebook's request to enforce the settlement with the Winklevoss twins and Narendra. The 9th Circuit agreed on Monday.

"At some point, litigation must come to an end," Kozinski wrote. "That point has now been reached."

Facebook deputy general counsel Colin Stretch said the company appreciated the court's careful consideration of the case, and was "pleased" it ruled in their favour.